D-\bar D mixing and rare D decays in the Littlest Higgs model with non-unitarity matrix

Abstract

We study the $D-\bar{D}$ mixing and rare D decays in the Littlest Higgs model. As the new weak singlet quark with the electric charge of 2/3 is introduced to cancel the quadratic divergence induced by the top-quark, the standard unitary $3\times 3$ Cabibbo-Kobayashi-Maskawa matrix is extended to a non-unitary $4\times 3$ matrix in the quark charged currents and Z-mediated flavor changing neutral currents are generated at tree level. In this model, we show that the $D-\bar{D}$ mixing parameter can be as large as the current experimental value and the decay branching ratio (BR) of $D\to X_u\text{ga}$ is small but its direct CP asymmetry could be $O(10$. In addition, we find that the BRs of $D\to X_u{\ell }^{+}{\ell }^{-}$, $D\to X_u\nu \bar{\nu }$ and $D\to {\mu }^{+}{\mu }^{-}$ could be enhanced to be $O(10^{-9})$, $O(10^{-8})$ and $O(10^{-9})$, respectively.

Comments: 18 pages, 6 figures, references added and updated, version to appear in Phys. Lett. B